Biplane X-ray angiograms, intravascular ultrasound, and 3D visualization of coronary vessels

Toward quantitative X-ray elastography of coronary arteries using flexural pulse waves

Dynamic elastography uses an imaging system to visualize the propagation of elastic waves, the speed of which is directly related to the elasticity felt by palpation. Very few studies have focused on X-ray elastography because of the technical challenges it poses: a planar image of an integration volume at a very slow sampling rate. We demonstrate that tracking a slow elastic wave guided along a one-dimensional structure could provide a possible solution. The recently discovered flexural pulse wave, which is naturally generated by heartbeats and propagates along arteries, is the perfect candidate for X-ray elastography. As it reflects the cardiovascular health of patients, arterial elasticity is a biomarker of high clinical interest. We first validate the method by measuring the elasticity in artery phantoms using X-ray. We then move on to data obtained in vivo on coronary arteries during a routine angiography examination. During coronary angiography, a catheter is used to inject an X-ray contrast dye into the patient's aorta. X-rays are then taken as the dye spreads through the coronary arteries. It shows the movement of the coronary arteries for a few seconds and provides an opportunity to follow the natural flexural pulse waves. The obtained Young's moduli for two patients are E = 38 ± 30 kPa and E = 38 ± 28 kPa, respectively. These preliminary results are expected to pave the way for X-ray elastography.

Brachytherapy seed localization using geometric and linear programming techniques

We propose an optimization algorithm to solve the brachytherapy seed localization problem in prostate brachytherapy. Our algorithm is based on novel geometric approaches to exploit the special structure of the problem and relies on a number of key observations which help us formulate the optimization problem as a minimization integer program (IP). Our IP model precisely defines the feasibility polyhedron for this problem using a polynomial number of half-spaces; the solution to its corresponding linear program is rounded to yield an integral solution to our task of determining correspondences between seeds in multiple projection images. The algorithm is efficient in theory as well as in practice and performs well on simulation data (approximately 98% accuracy) and real X-ray images (approximately 95% accuracy). We present in detail the underlying ideas and an extensive set of performance evaluations based on our implementation.

Towards a theory of a solution space for the biplane imaging geometry problem

Biplane angiographic imaging is a primary method for visual and quantitative assessment of the vasculature. In order to reliably reconstruct the three-dimensional (3D) position, orientation, and shape of the vessel structure, a key problem is to determine the rotation matrix R and the translation vector t which relate the two coordinate systems. This so-called Imaging Geometry Determination problem is well studied in the medical imaging and computer vision communities and a number of interesting approaches have been reported. Each such technique determines a solution which yields 3D vasculature reconstructions with errors comparable to other techniques. From the literature, we see that different techniques with different optimization strategies yield reconstructions with equivalent errors. We have investigated this behavior, and it appears that the error in the input data leads to this equivalence effectively yielding what we call the solution space of feasible geometries, i.e., geometries which could be solutions given the error or uncertainty in the input image data. In this paper, we lay the theoretical framework for this concept of a solution space of feasible geometries using simple schematic constructions, deriving the underlying mathematical relationships, presenting implementation details, and discussing implications and applications of the proposed idea. Because the solution space of feasible geometries encompasses equivalent solutions given the input error, the solution space approach can be used to evaluate the precision of calculated geometries or 3D data based on known or estimated uncertainties in the input image data. We also use the solution space approach to calculate an imaging geometry, i.e., a solution.

In-vivo coronary flow profiling based on biplane angiograms: influence of geometric simplifications on the three-dimensional reconstruction and wall shear stress calculation

Background

Clinical studies suggest that local wall shear stress (WSS) patterns modulate the site and the progression of atherosclerotic lesions. Computational fluid dynamics (CFD) methods based on in-vivo three-dimensional vessel reconstructions have recently been shown to provide prognostically relevant WSS data. This approach is, however, complex and time-consuming. Methodological simplifications are desirable in porting this approach from bench to bedside. The impact of such simplifications on the accuracy of geometry and wall shear stress calculations has to be investigated.

Methods

We investigated the influence of two methods of lumen reconstruction, assuming circular versus elliptical cross-sections and using different resolutions for the cross-section reconstructions along the vessel axis. Three right coronary arteries were used, of which one represented a normal coronary artery, one with "obstructive", and one with "dilated" coronary atherosclerosis. The vessel volume reconstruction was performed with three-dimensional (3D) data from a previously validated 3D angiographic reconstruction of vessel cross-sections and vessel axis.

Results

The difference between the two vessel volumes calculated using the two evaluated methods is less than 1 %. The difference, of the calculated pressure loss, was between 2.5% and 8.5% for the evaluated methods. The distributions of the WSS histograms were nearly identical and strongly cross-correlated (0.91–0.95). The good agreement of the results was confirmed by a Chi-square test.

Conclusion

A simplified approach to the reconstruction of coronary vessel lumina, using circular cross-sections and a reduced axial resolution of about 0.8 mm along the vessel axis, yields sufficiently accurate calculations of WSS.

A method for 3D reconstruction of coronary arteries using biplane angiography and intravascular ultrasound images

The aim of this study is to describe a new method for the three-dimensional reconstruction of coronary arteries and its quantitative validation. Our approach is based on the fusion of the data provided by intravascular ultrasound images (IVUS) and biplane angiographies. A specific segmentation algorithm is used for the detection of the regions of interest in intravascular ultrasound images. A new methodology is also introduced for the accurate extraction of the catheter path. In detail, a cubic B-spline is used for approximating the catheter path in each biplane projection. Each B-spline curve is swept along the normal direction of its X-ray angiographic plane forming a surface. The intersection of the two surfaces is a 3D curve, which represents the reconstructed path. The detected regions of interest in the IVUS images are placed perpendicularly onto the path and their relative axial twist is computed using the sequential triangulation algorithm. Then, an efficient algorithm is applied to estimate the absolute orientation of the first IVUS frame. In order to obtain 3D visualization the commercial package Geomagic Studio 4.0 is used. The performance of the proposed method is assessed using a validation methodology which addresses the separate validation of each step followed for obtaining the coronary reconstruction. The performance of the segmentation algorithm was examined in 80 IVUS images. The reliability of the path extraction method was studied in vitro using a metal wire model and in vivo in a dataset of 11 patients. The performance of the sequential triangulation algorithm was tested in two gutter models and in the coronary arteries (marked with metal clips) of six cadaveric sheep hearts. Finally, the accuracy in the estimation of the first IVUS frame absolute orientation was examined in the same set of cadaveric sheep hearts. The obtained results demonstrate that the proposed reconstruction method is reliable and capable of depicting the morphology of coronary arteries.

Assessment of vasoreactivity using videodensitometry coronary angiography

BACKGROUND

Previous studies demonstrated that the dysfunction of vasomotor tone (VT) is closely linked to the development of atherosclerosis and it is considered important in the very early stages of atherogenesis. Currently, the evaluation of VT relies on lumen changes in response to vasoactive stimuli using quantitative coronary angiography (QCA) based on geometric edge detection (ED). However, using ED for measuring lumen diameters is inherently associated with large uncertainties. Videodensitometry (VD) methods have important advantages over ED for QCA. The objective of this study was to investigate the reliability of VD and ED techniques in determining the effect of nitroglycerin (NTG) on cross-sectional area (CSA) and volume changes in a swine animal model for evaluating coronary vasoreactivity.

METHODS AND RESULTS

Coronary angiography was performed on four anesthetized swine. CSA and volume were measured in the left anterior descending (LAD) coronary artery using VD before and after intracoronary injection of 0.3 mg of NTG. CSA was also calculated using standard QCA based on ED. The average CSA changes in the proximal, middle and distal branches measured using VD were 23.83% (+/-10.76%), 30.78% (+/-18.39%), and 27.34% (+/-36.53%), respectively. Similarly, the average CSA changes in the proximal, middle, and distal branches measured using ED were 15.02% (+/-36.38%), 22.02% (+/-26.12), and 38.00% (+/-48.31%), respectively. The average lumen volume change measured using VD was 29.79% (+/-14.79%). In order to evaluate the relative reliability of the techniques. the significance of deviation (SOD) was calculated, which is the ratio of the change after NTG and the measurement error. The average SOD for CSA for all the branches based on VD and ED were 1.86 and 0.69, respectively. The SOD for volume measurement was 2.78.

CONCLUSIONS

Lumen changes measured by VD showed substantial improvement in reliability when compared to the ED. Moreover, VD can be used to measure substantially smaller changes in lumen dimension in response to vasoactive stimuli than the standard QCA based on ED. Finally, VD allows the measurement of arterial volume, which is not possible with ED.